A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Generalizes meander diagrams to virtual knots and introduces new invariants.
Resolving Schwartz's quadratic meander number conjecture
Counting meanders on surfaces of arbitrary genus, with precise asymptotics.
A meander is a topological configuration of a line and a simple closed curve in the plane (or a pair of simple closed curves on the 2-sphere) intersecting transversally. Meanders can be traced back to H. Poincaré and naturally appear in various areas of mathematics, theoretical physics and computational biology (in par…
New model for links uses meander diagrams and combinatorics.
We introduced concept of meander knots, 2-component meander links and multi-component meander links and derived different families of meander knots and links from open meanders with at most 16 crossings. We also defined semi-meander knots (or knots with ordered Gauss code) and their product.
Study bounds growth rate of irreducible meanders, showing proportion vanishes.
Study on a new class of meanders with tangential intersections.
New estimate of semimeander complexity for knots with more than 10 crossings.
The problem of which Gauss diagram can be realized by plane curves is an old one and has been solved in several ways. In this paper, we present a direct approach to this problem. We show that needed conditions for realizability of a Gauss diagram can be interpreted as follows "the number of exits = the number of entran…
A meander of order n is a simple closed curve in the plane which intersects a horizontal line transversely at 2n points. (Meanders which differ by an isotopy of the line and plane are considered equivalent.) Let Gamma_n be the Cayley graph of the symmetric group S_n as generated by all (n choose 2) transpositions. Let …
In his 1985 paper Sullivan sketched a proof of his structural stability theorem for differentiable group actions satisfying certain expansion-hyperbolicity axioms. In this paper we relax Sullivan's axioms and introduce a notion of "meandering hyperbolicity" for group actions on geodesic metric spaces. This generalizati…
Minimal constructions of meanders and hyperelliptic pillowcase covers help in understanding ratio-optimizing pseudo-Anosovs.
We found a way to code meanders and show they are idempotent.
Jablan and Radović originally defined two invariants called the Meander number and OGC number of knots for certain classes of knots. We generalize these definitions to all knots and name the straight number and contained straight number of a knot, respectively, and prove they are well defined. We answer two questions a…
We study decomposition into simple arcs (i. e., arcs without self-intersections) for diagrams of knots and spatial graphs. In this paper, it is proved in particular that if no edge of a finite spatial graph is a knotted loop, then there exists a plane diagram of such that (i) each edge of is represented…
The paper examines circle graphs of Gauss diagrams and finds counterexamples to previous descriptions.
We propose a simple stochastic model for the dynamics of a limit order book, extending the recent work of Cont and de Larrard (2013), where the price dynamics are endogenous, resulting from market transactions. We also show that the conditional diffusion limit of the price process is the so-called Brownian meander.
We study collections of planar curves that yield diagrams for all knots. In particular, we show that a very special class called potholder curves carries all knots. This has implications for realizing all knots and links as special types of meanders and braids. We also introduce and apply a method to compare the effici…
This note re-addresses the Paris barrier options proposed by Yor and collaborators and their valuation using the Laplace transform approach. The notion of Paris barrier options, based on excursion theory and using the Brownian meander, is extended such that their valuation is now possible at any point during their life…
In this paper, we demonstrated a practical application of realistic river image generation using deep learning. Specifically, we explored a generative adversarial network (GAN) model capable of generating high-resolution and realistic river images that can be used to support modeling and analysis in surface water estim…
Investigates Q value evolution in Stable Baselines for DQL in simple vs complex environments.
Study uses DMD to analyze oceanic features in Strait of Gibraltar.
We define and compare several natural ways to compute the bridge number of a knot diagram. We study bridge numbers of crossing number minimizing diagrams, as well as the behavior of diagrammatic bridge numbers under the connected sum operation. For each notion of diagrammatic bridge number considered, we find crossing …
Spatial embeddings of planar graphs can have higher unknotting numbers than crossing numbers.
The unknotting number of a knot is the minimum number of crossings one must change to turn that knot into the unknot. The algebraic unknotting number is the minimum number of crossing changes needed to transform a knot into an Alexander polynomial-one knot. We work with a generalization of unknotting number due to Math…
The paper bounds the handle number of sutured manifolds using Morse-Novikov numbers and tunnel numbers.
New measure shows how links can be untangled as twists increase.
New number bounds knot complexity, including unknotting and crosscap numbers.
We give an upper bound for the dealternating number of a closed 3-braid. As applications, we determine the dealternating numbers, the alternation numbers and the Turaev genera of some closed positive 3-braids. We also show that there exist infinitely many positive knots with any dealternating number (or any alternation…
Paper shows that for torus knots, the pinch number equals the unoriented band unknotting number.
Delta-unlinking number measures how to unlink algebraically split links.
Study on knot properties, showing relation between unknotting and crossing numbers.
Odd crossing numbers and even rotation numbers for cycles in plane immersions.
Study computability of real numbers from group properties.
We define the basket number, the flat plumbing number and the flat plumbing basket number of a link. Then we provide some upperbounds for these plumbing numbers by using Seifert's algorithm. We study the relation between these plumbing numbers and the genera of links.
The aim of the present paper is to prove that the minimal number of virtual crossings for some families of virtual knots grows quadratically with respect to the minimal number of classical crossings. All previously known estimates for virtual crossing number were principally no more than linear in the number of classic…
This paper calculates stick numbers for rail arcs and knot classes.
The (ordinary) unknotting-number of 1-dimensional knots, which is defined by using the crossing-change, is a very basic and important invariant. It is very natural to consider the `unknotting-number' associated with other local-moves on n-dimensional knots, where n is a natural number. In this paper we prove the follow…
In this paper we investigate the unlinking numbers of 10-crossing links. We make use of various link invariants and explore their behaviour when crossings are changed. The methods we describe have been used previously to compute unlinking numbers of links with crossing number at most 9. Ultimately, we find the unlinkin…
This paper is about the clock number of a knot. First we define the clock number by using states of a knot defined by Kauffman. Next we show that if K is a prime knot, its clock number is greater than or equal to its crossing number. Finally we prove that its clock number is equal to its crossing number if and only if …
We study three knot invariants related to smoothly immersed disks in the four-ball. These are the four-ball crossing number, which is the minimal number of normal double points of such a disk bounded by a given knot; the slicing number, which is the minimal number of crossing changes to a slice knot; and the concordanc…
For a knot the cube number is a knot invariant defined to be the smallest for which there is a cube diagram of size for . There is also a Legendrian version of this invariant called the \emph{Legendrian cube number}. We will show that the Legendrian cube number distinguishes the Legendrian left hand toru…
New insights into knot fusion numbers via cabling.
Links with minimum tunnel number have one less component than their number of parts.
New bounds and examples for sphere unknotting numbers.
A rational linear combination of Chern numbers is an oriented diffeomorphism invariant of smooth complex projective varieties if and only if it is a linear combination of the Euler and Pontryagin numbers. In dimension at least three only multiples of the top Chern number, which is the Euler characteristic, are invarian…
We give lower bounds for the tunnel number of knots and handlebody-knots. We also give a lower bound for the cutting number, which is a "dual" notion to the tunnel number in the handlebody-knot theory. We provide necessary conditions for constituent handlebody-knots by using -family of quandles colorings. The above …